Sometime in the last decade, coleslaw, so familiar a fixture of every Boxing Day buffet and summer picnic, has been rebranded. And every time I see a "slaw" sitting chirpily on the menu, a grumpy, Victor Meldrew-like surge of irritation courses through me. The Berni Inn salad bar never called it slaw. My dad never put ham and slaw sandwiches in our picnics. If it doesn't have cabbage in it then it's not coleslaw: it's a salad. End of rant.

Making myself even more comfortable in pedants' corner, coleslaw is a corruption of the Dutch koolsla, meaning cabbage salad, and arrived here via the USA. Cabbage was, according to the Oxford Encylopedia of Food and Drink in America, a popular crop "throughout the colonies", and Dutch settlers, who grew it "extensively along the Hudson River" liked to serve it in the familiar, old-country way: the first mention of coleslaw in the USA dates from 1785.

Early versions seem only to have used a vinaigrette, but mayonnaise now seems to be the standard dressing, in Britain at least – preferably the gloopy sugary kind that smothers all other flavours, leaving you unsure whether you're eating cabbage or carrot. The occasional chunks of raw onion, however, usually make themselves known. Perhaps, thinking about it, this explains the rebranding exercise. But I'm determined to make coleslaw cool again. Or, at least, nice.

The cabbage: crucifer rising

Constance Spry recipe coleslaw. Photograph: Felicity Cloake

White cabbages rather than green are favoured, probably because of their superior crunch, although Constance Spry reckons that completely white cabbages have a "particularly sweet and nutty flavour". Valentine Warner uses a mixture of white and red in his recipe in The Good Table, which looks very striking – a Cooks Illustrated recipe suggests red or green, so I use all red, but find the flavour too sweet.

Constance suggests immersing the shredded cabbage in ice cold water, preferably overnight, before use. I wonder if this is to perk up an old timer or even to dull the cabbage's slightly sulphurous flavour: either way, I can't see it makes much difference to the finished dish. Cooks Illustrated salts their cabbage until it wilts, then rinses and pats dry before use. This softens it pretty effectively, but I like a bit of crunch – as long as you've shredded it finely enough, you should be able to use it straight away.

I, however, am not going to. Simon Hopkinson and Lindsey Bareham, writing in The Prawn Cocktail Years, marinate their cabbage in sugar, salt and vinegar for an hour, and then wring it out before use. This generates a surprising amount of liquid, but, more interestingly as far as I'm concerned, gives it a delicious but subtle tanginess.

The cut

Prawn Cocktail Years recipe coleslaw. Photograph: Felicity Cloake

Most recipes suggest shredding the cabbage finely, but Simon and Lindsey grate it "on the finest shredding blade of a food processor". Mine turns out rather mushy, although this could be the fault of my machine. In any case, unless you're making coleslaw for the 5,000, it's easier to chop it by hand, rather than giving yourself extra washing up by faffing about with machinery. (In the interests of fairness, I must add here that one of my housemates actively enjoys the slightly pre-masticated texture, and commandeers the whole lot for her packed lunch.)

Valentine Warner, who, like almost all the recipes I try (Constance Spry being the only cabbage purist) uses carrot in his coleslaw, suggests peeling it into thin slices, and then cutting these into strips to match the cabbage. It's a bit more time-consuming than getting out the grater, but, both visually and texturally, the results are far more pleasing.

The dressing

Claudia Roden recipe coleslaw. Photograph: Felicity Cloake

Apart from Claudia Roden, who, in her Book of Jewish Food says she finds coleslaw "most pleasing simply dressed with oil and vinegar," all the recipes I try are for creamy coleslaws. I do like her version – I often make a quick coleslaw from things that have outstayed their welcome in the salad tray, tossed with vinaigrette – but, according to my testing panel, a classic British coleslaw deserves better.

Valentine Warner makes a quick mayonnaise in the food processor, using egg yolks, sunflower oil, English and Dijon mustards and white wine vinegar, with 2 tablespoons of yoghurt stirred in at the end. I find his dressing rather too vinegary although I'm relieved it's not quite as sweet as the cooked dressing recommended by Constance Spry. This is made by heating sugar, flour, salt, mustard and vinegar together (I use malt vinegar, because I suspect that's what most people would have had in the house in 1956 when her Cookery Book was originally published), and then beating them into egg and butter, and stirring in cream to dilute. While it certainly has punch in the flavour department, it's also incredibly rich: Simon and Lindsey's homemade mayonnaise seems light in comparison. (Although it might seem like a lot of work, making your own mayonnaise is really worthwhile here, because most ready-made versions tend to be fairly heavy on the vinegar.)

Cooks Illustrated recipe coleslaw. Photograph: Felicity Cloake

The buttermilk dressing used in Cooks Illustrated is a traditional choice in the American south, in this case thickened with mayonnaise and sour cream, and flavoured with cider vinegar and mustard. Tangy and surprisingly fresh, this feels like a good coleslaw for a hot day, and, perhaps by association, I find myself thinking it would be a very pleasant partner to fried chicken, if I ever work up an appetite for another helping.

When it comes to flavour, thanks to its double dressing the Prawn Cocktail Years coleslaw is by far and away the panel's favourite. The cabbage and carrot are very lightly pickled from their earlier marinade, so there's no need to pack the homemade mayonnaise with vinegar and sugar, and the contrast between the two dressings makes it a far more interesting salad to eat. And, although I like a certain amount of crunch, the pickling process does soften things slightly.

Most coleslaw recipes employ mustard, either Dijon or English, in the dressing, but in a flash of inspiration, I'm substituting horseradish instead: the peppery heat works better, I think, with the slight bitterness of the cabbage.

The onion question

Valentine Warner recipe coleslaw. Photograph: Felicity Cloake

I'll come out and admit it now: I don't like raw onion in my coleslaw. Not when it's red and you "rinse away its attitude" before use as Valentine Warner suggests, not when it's a finely minced shallot à la Cooks Illustrated, and particularly not when it's a grated sweet onion as in Claudia Roden's recipe. It's just too strong.

I can't deny, however, that the sweet and sour tang of a good coleslaw is a good complement for a subtler onion flavour, but the chives that Simon and Lindsey use get lost. In the end, I settle for finely chopped spring onion, which will deliver the requisite alliaceousness without the harshness I find so troubling.

Claudia grates green pepper into her coleslaw, although the fact it's marked as "optional" suggests she's aware that it's not really a classic addition. The flavour seems to belong to a different cuisine. Ditto the dill that Constance Spry suggests adding, or the parsley in the Cooks Illustrated recipe: they're nice, but they do change the character of the entire dish. I'll let the spring onions bring greenery to the party.

Perfect coleslaw

Felicity's perfect coleslaw. Photograph: Felicity Cloake

As we head into autumn proper, this colourful coleslaw is a excellent way to get British seasonal produce on the table – and so much better with baked ham or a pie than boiled cabbage and mushy carrot medallions.

1. Cut the woody core from the cabbage quarters and then shred them as finely as you have the patience for. Peel the carrots and then use the peeler to cut them into long thin slices. Shred these into strips, and put them, along with the cabbage, in a colander. Add the salt, sugar and vinegar, toss together, and leave in the sink to drain for an hour.

2. Meanwhile, make your mayonnaise. Mix in the horseradish to taste. Press down the vegetables to squeeze out any excess liquid, then tip into a bowl and add the spring onion. Spoon in the mayonnaise and toss together, then serve.

Why has coleslaw become so ubiquitous – and when did it first became popular in this country? Are you a cabbage purist, or do you prefer to add other veg? Vinaigrette or mayonnaise? And will anyone stick up for the ready-made gloop?